Find the HCF of the smallest composite number and the smallest prime number?

The smallest composite number is 4.

The smallest prime number is 2.

Prime factorisation of 4 is given as $4=2^2$.

Prime factorisation of 2 is given as $2=2^1$.

HCF is the minimum power of each prime factor that is common to both numbers. In this case, the only common prime factor is 2, and its minimum power is 1.

So, the HCF of 4 and 2 is $2^1=\mathbf{2}$.